DIRECT TRAJECTORY OPTIMIZATION USING NONLINEAR PROGRAMMING AND COLLOCATION

An algorithm for the direct numerical solution of an optimal control problem is given. The method employs cubic polynomials to represent state variables, linearly interpolates control variables, and uses collocation to satisfy the differential equations. This representation transforms the optimal control problem to a mathematical programming problem which is solved by sequential quadratic programming. The method is easy to program for a very general trajectory optimization problem and is shown to be very efficient for several sample problems. Results are compared with solutions obtained with other methods.

[1]  Michael A. Saunders,et al.  User''s guide for NPSOL (Ver-sion 4.0): A FORTRAN package for nonlinear programming , 1984 .

[2]  J. Betts,et al.  Solving the optimal control problem using a nonlinear programming technique. I - General formulation , 1984 .

[3]  Numerical computation of optimal atmospheric trajectories involving staged vehicles , 1982 .

[4]  Philip E. Gill,et al.  Practical optimization , 1981 .

[5]  C. Hargraves,et al.  Numerical Computation of Optimal Atmospheric Trajectories , 1981 .

[6]  D. Kraft,et al.  On the choice of minimization algorithms in parametric optimal control problems , 1981 .

[7]  S. W. Paris,et al.  Application of an advanced trajectory optimization method to ramjet propelled missiles , 1980 .

[8]  Carl de Boor,et al.  A Practical Guide to Splines. , 1980 .

[9]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[10]  Shih-Ping Han,et al.  Superlinearly convergent variable metric algorithms for general nonlinear programming problems , 1976, Math. Program..

[11]  David G. Hull,et al.  Computation of optimal aircraft trajectories using parameter optimization methods , 1975 .

[12]  Klaus H. Well,et al.  Approximate Solution of Optimal Control Problems Using Third Order Hermite Polynomial Functions , 1974, Optimization Techniques.

[13]  L. Shampine,et al.  A collocation method for boundary value problems , 1972 .

[14]  Arthur E. Bryson,et al.  Energy-state approximation in performance optimization of supersonic aircraft , 1969 .

[15]  F. Johnson,et al.  Approximate finite-thrust trajectory optimization. , 1969 .

[16]  A. V. Balakrishnan,et al.  On a new computing technique in optimal control theory and the maximum principle. , 1968, Proceedings of the National Academy of Sciences of the United States of America.

[17]  G. Franklin,et al.  A second-order feedback method for optimal control computations , 1967, IEEE Transactions on Automatic Control.

[18]  A. E. Bryson,et al.  A Steepest-Ascent Method for Solving Optimum Programming Problems , 1962 .

[19]  H. Kelley.  Method of Gradients , 1962 .